Seniority Dynamics

Each person in the simulation has a fixed tenure (how long they've been around) and a fixed competence (how good they are). Their rank evolves over time pulled by three competing forces — plus random noise. The question is: which force wins?

In almost every real organization, the seniority force wins. The simulation lets you dial up each force independently to see why, and to find the regimes where merit can compete.

The Equation

$$dr_i = \bigl[\,\alpha(c_i - \bar{c}) \;-\; \beta(r_i - s_i) \;-\; \gamma H_i\,\bigr]\,dt \;+\; \sigma\,dW_i$$

$$H_i = \tfrac{1}{N}\sum_{j}\max(0,\,\tau_j - \tau_i)\cdot\max(0,\,r_i - r_j)$$

Read it as: the change in your rank each instant = merit pull + seniority pull + holdup pull + luck.

Every Term Explained

$\alpha(c_i - \bar{c})$

Meritocratic drift α slider

Pulls your rank up if you're above-average competence, down if below. α controls how much the org actually rewards ability. In most orgs, α is small — talent is noticed slowly and incompletely.

$-\beta(r_i - s_i)$

Seniority restoring force β slider

Pulls your rank back toward $s_i$ — the rank your tenure alone predicts. Think of it as a spring: the further you've drifted from "your place in line," the harder it pulls you back.

Where does this spring come from? Three sources: (1) deferred compensation — firms underpay juniors and overpay seniors on purpose; the future overpayment is a bond that breaks if seniority is skipped (Lazear 1979). (2) Tournament prizes — the pay gap between ranks is the incentive for everyone below; inverting rank compresses the prize (Lazear & Rosen 1981). (3) Fairness norms — everyone watching recalibrates their expectations when the line is jumped (Akerlof & Yellen 1990).

$-\gamma H_i$

Insider holdup γ slider

$H_i$ is nonzero only when junior $i$ is currently outranking some senior $j$. In that case, a force pushes $i$ back down — proportional to how far above $j$ they've risen and how much more senior $j$ is.

This is your "hostage" intuition (Lindbeck & Snower 1984): seniors who've been displaced can withhold cooperation, context, and access, making the junior's contributions less legible to the org. The formula captures the magnitude of their leverage.

$\sigma\,dW_i$

Noise σ slider

Random shocks — politics, visibility, project luck, manager turnover. Not IQ-on-a-bad-day. More like "a key project landed on your desk this quarter that made you look great or terrible." Not essential to the dynamics; set σ ≈ 0 for clean motion.

The Variables on Each Dot

Parameter Regimes (the 5 tabs)

Var	Name	What it means
$\tau_i$	Tenure	Fixed. Determines x-position on the scatter. Grows very slowly. The "age ordering."
$c_i$	Competence	Fixed. Shown as dot color — blue = low, red = high. Drawn from a distribution at start.
$r_i$	Rank	The state variable — the only thing that moves. Determines y-position. This is what the SDE governs.
$s_i$	Seniority target	The rank $\tau_i$ predicts based on tenure order alone. The spring pulls $r_i$ toward $s_i$.
$H_i$	Holdup force	Computed from the current positions of all other agents. High when junior $i$ is sitting above many seniors.

Seniority dominates

α/β = 0.2, γ moderate

After mutiny, cloud snaps back to diagonal fast. Blue τ(rank, tenure) recovers fully. The normal org.

Meritocracy

α/β = 6, γ ≈ 0

Dots sort by color (red up, blue down). Orange τ(rank, comp) stays high. Tenure order is irrelevant.

Holdup fortress

γ = 2.0, β = 0.2

β is weak, so recovery after mutiny is driven by holdup alone — slower, lumpier, but still wins.

Phase boundary

α ≈ β, γ small

Neither wins cleanly. After mutiny the cloud settles loosely — both τ values are moderate. The interesting middle.

Scene 2: The Replicator Layer

Each senior now carries a hoarding intensity $h_i \in [0,1]$ — how hard they're working to withhold institutional knowledge. The gold ring around a senior dot shows $h_i$.

$$\frac{dh_i}{dt} = \varepsilon \cdot v_i \;-\; \delta \cdot h_i$$

$v_i$ = number of juniors currently outranking senior $i$

When a mutiny strikes, violation counts spike → hoarding intensifies → holdup force strengthens → seniority order is restored faster → violations drop → hoarding decays. The equilibrium defends itself endogenously. This is why top-down meritocratic reshuffles tend to fail: they trigger the very behavior (knowledge-hoarding) that reverses them.

The Key Ratio to Remember

α/β is the single number that determines which attractor you're in. Below ~0.5: seniority wins. Above ~2.0: merit wins. In between: mixed, sensitive to perturbations. Most real organizations sit around 0.1–0.3.